Answers to Some Questions About Increments of a Wiener Process

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Some Results on Increments of the Wiener Process

Let λ(T,aT ,α) = { 2aT [ log T aT + α log log T + (1− α) log log aT ]}− 2 where 0 ≤ α ≤ 1 and {W (t), t ≥ 0} be a standard Wiener process. This paper studies the almost sure limiting behaviour of sup 0≤t≤T−aT λ(T,aT ,α)|W (t+aT )−W (t)| as T −→∞ under varying conditions on aT and T aT .

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ژورنال

عنوان ژورنال: The Annals of Probability

سال: 1986

ISSN: 0091-1798

DOI: 10.1214/aop/1176992366